Aerodynamic Characterization of Hypersonic Transportation Systems and Its Impact on Mission Analysis

energies

Article Aerodynamic Characterization of Hypersonic Transportation Systems and Its Impact on Mission Analysis

Nicole Viola 1, Pietro Roncioni 2 , Oscar Gori 1 and Roberta Fusaro 1,*

1 Mechanical and Aerospace Engineering Department, Politecnico di Torino, 10129 Turin, Italy; [email protected] (N.V.); [email protected] (O.G.) 2 Aerothermodynamics Department, Centro Italiano Ricerche Aerospaziali, 81043 Capua, Italy; [email protected] * Correspondence: [email protected]

Abstract: This paper aims to provide technical insights on the aerodynamic characterization activities performed in the field of the H2020 STRATOFLY project, for the Mach 8 waverider reference configuration. Considering the complexity of the configuration to be analyzed at conceptual/preliminary design stage, a build-up approach has been adopted. The complexity of the aerodynamic model increases incrementally, from the clean external configuration up to the complete configuration, including propulsion systems elements and flight control surfaces. At each step, the aerodynamic analysis is complemented with detailed mission analysis, in which the different versions of the aerodynamic databases are used as input for the trajectory simulation. eventually, once the contribution to the aerodynamic characterization of flight control surfaces is evaluated, stability and trim analysis is carried out. The comparison of the results obtained through the different mission analysis campaigns clearly shows that the accuracy of aerodynamic characterization may determine the feasibility or unfeasibility of a mission concept. Citation: Viola, N.; Roncioni, P.; Gori, O.; Fusaro, R. Aerodynamic Keywords: aerodynamic characterization; mission analysis; hypersonic civil transport Characterization of Hypersonic Transportation Systems and Its Impact on Mission Analysis. Energies 2021, 14, 3580. https://doi.org/ 1. Introduction 10.3390/en14123580 Hypersonic cruisers are currently considered as the long-term future of long-range civil aviation. The expected high-level performance are challenging engineers and scientists Academic Editor: Adonios Karpetis from around the world in different technological and operational areas. Despite the wide range of solutions that are emerging for these challenges, everybody agrees on Received: 3 May 2021 the urgent need to improve the conceptual design stage, defining innovative and agile Accepted: 12 June 2021 Published: 16 June 2021 design methodologies able to capture all the most impacting design, performance, and operational characteristics since the beginning of the process and implementing multi-

Publisher’s Note: MDPI stays neutral fidelity modelling strategies. The development of such an integrated methodology is with regard to jurisdictional claims in one of the outcomes of the STRATOFLY Project, a Horizon 2020 Project funded by the published maps and institutional affil- European Commission in 2018, aimed at assessing the potential of this type of high-speed iations. civil transport to reach TRL6 by 2035, with respect to key technological, societal and economical aspects, such as thermal and structural integrity, low-emissions combined propulsion cycles, subsystems design and integration including smart energy management, environmental aspects impacting climate change, noise emissions and social acceptance, and economic viability accounting for safety and human factors. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. The aerodynamic characterization is one of the crucial activities of a multidisciplinary This article is an open access article conceptual design approach for high-speed vehicles. It will support the definition and distributed under the terms and characterization of the aircraft configuration, suggesting possible improvements necessary conditions of the Creative Commons to meet performance and operational requirements. Nowadays, the high-speed air and Attribution (CC BY) license (https:// space transportation systems are experiencing a revolution in the design process, which is creativecommons.org/licenses/by/ resulting in highly innovative and integrated concepts, able to push the performance barrier 4.0/). beyond the limits. This is especially visible in the case of hypersonic civil transportation

Energies 2021, 14, 3580. https://doi.org/10.3390/en14123580 https://www.mdpi.com/journal/energies Energies 2021, 14, x FOR PEER REVIEW 2 of 26

Energies 2021, 14, 3580 2 of 28 which is resulting in highly innovative and integrated concepts, able to push the performance barrier beyond the limits. This is especially visible in the case of hypersonic civil transportationsystems, such as systems, the STRATOFLY such as the MR3 STRATO concept,FLY where MR3 the concept, need to where meet athe set need of challenging to meet a settechnical of challenging and operational technical requirements and operational may requirements impose the adoption may impose of highly the adoption integrated of highlywaverider integrated configurations waverider [1 –config4]. Inurations these cases, [1–4]. it In is these fundamental cases, it is to fundamental support the vehicleto sup- portdesign the processvehicle design with a process set of aerodynamic with a set of investigationsaerodynamic investigations and mission and analysis, mission with anal- an ysis,increasing with an level increasing of complexity. level of In complexity. this context, In thisthispaper context, aims this at paper presenting aims at the presenting results of the results build-up of the approach build-up adopted approach in theadopt frameworked in the framework of the H2020 of STRATOFLYthe H2020 STRATOFLY Project, to Project,improve to the improve configuration the configuration of the reference of the vehicle, reference incrementally vehicle, incrementally increasing theincreasing complexity the complexityof the aerodynamic of the aerodynamic model, from model, the clean from externalthe clean configuration external configuration up to the up complete to the completeconfiguration, configuration, including propulsionincluding propulsion systems elements systems and elements flight control and flight surfaces. control At eachsur- faces.step, theAt each aerodynamic step, the aerodynamic analysis is complemented analysis is complemented with detailed with mission detailed analysis, mission in which analysis,the different in which versions the different of the versions aerodynamic of the databasesaerodynamic are databases used as input are used for the as trajectoryinput for thesimulation trajectory (see simulation Figure1). (see Figure 1).

Figure 1. IncrementalIncremental approach to Aerodynamic CharacterizationCharacterization and Mission Analysis investigations.investigations.

Specifically,Specifically, after this this short short introduction, introduction, Section Section 22 brieflybriefly provides provides the the reader reader with with a summarya summary description description of of the the STRATOFLY STRATOFLY MR3 MR3 vehicle vehicle configuration configuration and and its reference mission. Then, Then, Section 33 focusesfocuses onon thethe step-by-stepstep-by-step aerodynamicaerodynamic characterizationcharacterization ofof thethe vehicle from the clean to thethe completecomplete vehiclevehicle configuration.configuration. Even if the aerodynamicaerodynamic characterization approach is well-known, Section 33 pointspoints outout specificspecific innovativeinnovative aspectsaspects which have been introduced to better cope wi withth the analysis of a highly integrated wa- wa- verider configuration configuration at conceptual design level.level. The build-up approach starts from the investigationinvestigation of of the the clean clean configuration, configuration, which which consists consists of of the the external external vehicle vehicle layout, layout, in- in- cluding empennagesempennages and and undeflected undeflected control control surfaces. surfaces. Inviscid Inviscid CFD CFD simulation simulation techniques tech- niquesare applied are applied to better to better describe describe the subsonic the subs andonic transonicand transonic regime. regime. Complementary, Complementary, an anupdated updated mathematical mathematical formulation formulation for for viscous viscou effects effect corrective corrective factor factor is disclosed. is disclosed. In the In thefollowing following steps steps of the of build-upthe build-up approach, approach, the contributions the contributions of the of internal the internal flow-path flow-path of the ofpropulsive the propulsive system, system, and of and the deflectedof the defle controlcted control surfaces surfaces are evaluated are evaluated and added and added to the toclean the configuration.clean configuration. These lastThese steps last are steps extremely are extremely important important for highly for integratedhighly integrated vehicle vehiclewaverider waverider configurations configurations where the where propulsive the propulsive subsystems subsystems flow-path flow-path may represent may repre- up to sent30–40% up to of 30–40% the vehicle of the available vehicle volume available and volume where and non-conventional where non-conventional flight control flight surfaces con- trolarchitecture surfaces mayarchitecture be adopted. may Thebe adopted. importance The of importance properly addressing of properly these addressing contributions these contributionsfor the aerodynamic for the characterizationaerodynamic characterization of the vehicle is of testified the vehicle in Section is testified4, the comparisonin Section 4, theof the comparison results obtained of the throughresults obtained the different through mission the analysisdifferent campaigns mission analysis clearly campaigns shows that clearlythe accuracy shows of that aerodynamic the accuracy characterization of aerodynamic may characterization determine the feasibilitymay determine or unfeasibility the feasi- of the mission concept. In this context, special attention is devoted to the longitudinal bility or unfeasibility of the mission concept. In this context, special attention is devoted stability analysis, which shows that in order to meet the high-level design and operational to the longitudinal stability analysis, which shows that in order to meet the high-level requirements (such as maximum take-off weight and range), the stability concept should

Energies 2021, 14, 3580 3 of 28

be relaxed into the low supersonic speed regime. Finally, ideas for future investigations are reported and main conclusions are drawn.

2. STRATOFLY MR3: Vehicle and Mission Overview The STRATOFLY MR3 vehicle is the result of research activities carried out by several international partners in the framework of the Horizon 2020 STRATOFLY Project funded by the EC since June 2018. Beneﬁtting from the heritage of past European funded projects and, in particular, from the LAPCAT II project led by ESA [1], the waverider conﬁguration has

Energies 2021, 14, x FOR PEER REVIEWbeen adopted and investigated in-depth throughout all ﬂight phases. STARTOFLY MR34 of 26 is a highly integrated system, where propulsion, aerothermodynamics, structures and on-board subsystems are strictly interrelated to one another, as highlighted in Figure2a [2,3].

(a) (b)

FigureFigure 2. 2.(a)( aSTRATOFLY) STRATOFLY MR3 MR3 Vehicle Vehicle and and (b (b) Idealized) Idealized Mission Mission Concept. Concept.

AnLooking overview at theof the configuration, vehicle dimensions the STRATOFLY is also reported MR3 design in Table is driven1 [2]. by its peculiar mission concept, which can be summarized as follows: STRATOFLY MR3 will be able Tableto fly 1. alongSTRATOFLY long-haul MR3 routes vehicle reaching dimensions. Mach 8 during the cruise phase at a stratospheric altitude (h > 30,000 m) carrying 300 passengers as payload. Figure2a shows STRATOFLY Parameter Value Unit of Measure MR3 external configuration. STRATOFLY MR3 has a waverider configuration with the Length 94 m engines and related air duct embedded into the airframe and located at the top. The integrationWingspan of the propulsive system at the41 top of the vehicle allows maximizationm of the availableWing planform surface for lift generation without 1365 additional drag penalties,m thus increasing the aerodynamicAspect ratio efficiency, and it allows ~1 optimizing the internal volume. - This layout guarantees furthermore to expand the jet to a large exit nozzle area without the need to 3.perturb Aerodynamic the external Characterization shape which would lead to extra pressure drag. The mission profile (Figure2b) is based on the LAPCAT reference [ 5]. During the 3.1.first Methodology part of the Overview mission the ATR engines are used and the vehicle performs the first climb phase,This which section terminates aims at describing at Mach = the 0.95 meth andodology at an altitude used betweento perform 11 andthe aerodynamic 13 km. The air characterizationturbo–rocket (ATR) of the is STRATOFLY a particular caseMR3 of vehicle turbine-based concept. combinedConsidering cycles that cycle the project engines dealswhich with brings the conceptual together elements and preliminary of the turbojet design and of the rocket vehicl motorse, an andincremental provides build-up a unique approachset of performance has been exploited characteristics. [6–9]. The This approach engine starts offers from a high the thrust-to-weightinvestigation of the ratio clean and configurationspecific thrust which over consists a wide rangeof the of external speed andvehicle altitude, layout, constituting including anempennages excellent choice and undeflectedas an accelerator control enginesurfaces. up Then, to high-supersonic when additional speeds. details Then, on the the integration vehicle performs of the pro- the pulsivesubsonic flow-path cruise. and This of phase the control is needed surface to prevent deflections a sonic are boom available, while the flying aerodynamic on land. A databaseconstraint is improved on the distance with new flown contributions. from the departure In details, site the should lift co beefficient considered is evaluated to fulfill addingthis requirement: to the clean configuration, the subsonic cruise the contri phasebutions ends whento lift of the al vehiclel the control is at surfaces 400 km from 𝑖 (i.e., the departure airport. Then, the supersonic climb starts, and the vehicle accelerates up to ∑ ∆𝐶 ). Similarly, the drag coefficient is evaluated adding to the clean configuration, theMach contributions = 4. At the to end drag of this of all phase, the thecontrol ATR surfaces. enginesare Finally, turned the off y-moment and the DMR coefficient is activated is evaluatedto accelerate by summing up to Mach to =the 8. value Dual Modeof the Ramjetclean configuration, engine (DMR) the is the single high-speed effects of engine the controlthat can surfaces, be operated and the in bothadditional ramjet effects and scramjet of the misalignment modes. The next of phasethrust isvector the hypersonic with respect to the longitudinal vehicle axis.

𝐶 𝐶 ∆𝐶 (1)

𝐶 𝐶 ∆𝐶 ∆𝐶 ∆𝐶 (2)

𝐶 𝐶 ∆𝐶 ∆𝐶 (3)

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cruise: in case of a Europe to Asia or Australia mission, the vehicle should point towards the Bering strait, then it ﬂies over the Paciﬁc Ocean to reach the designated destination. The cruise altitude should be in the range from 30 to 35 km. Eventually, the engines are turned off and the vehicle performs the descent towards the landing site. An overview of the vehicle dimensions is also reported in Table1[2].

Table 1. STRATOFLY MR3 vehicle dimensions.

Parameter Value Unit of Measure Length 94 m Wingspan 41 m Wing surface 1365 m2 Aspect ratio ~1 -

3. Aerodynamic Characterization 3.1. Methodology Overview This section aims at describing the methodology used to perform the aerodynamic characterization of the STRATOFLY MR3 vehicle concept. Considering that the project deals with the conceptual and preliminary design of the vehicle, an incremental build-up approach has been exploited [6–9]. The approach starts from the investigation of the clean configuration which consists of the external vehicle layout, including empennages and undeflected control surfaces. Then, when additional details on the integration of the propulsive flow-path and of the control surface deflections are available, the aerodynamic database is improved with new contributions. In details, the lift coefficient is evaluated adding to the clean configuration, the contributions to lift of all the control surfaces i (i.e., n ∑ (∆CL)i ). Similarly, the drag coefficient is evaluated adding to the clean configuration, i = 1 the contributions to drag of all the control surfaces. Finally, the y-moment coefficient is evaluated by summing to the value of the clean configuration, the single effects of the control surfaces, and the additional effects of the misalignment of thrust vector with respect to the longitudinal vehicle axis.

n CL = (CL)clean + ∑ (∆CL)i (1) i = 1

n C = (C ) + (∆C ) + (∆C ) + (∆C ) (2) D D cleaninv D viscext D viscint ∑ D i i = 1 n = + + CMy CMy clean ∑ ∆CMy i ∆CMy T (3) i = 1 When dealing with conceptual design, due to the time and budget constraints, simplified approaches are preferred for the aerodynamic characterization, such as the Panel Methods. However, in this case, taking into account the complexity of the vehicle configuration, and remembering that one of the main goals of the H2020 STRATOFLY Project is to better investigate the behavior of the vehicle concept in subsonic and transonic speed regimes, simplified CFD simulation campaigns have been selected, as the most appro- priate approach. Specifically, inviscid CFD simulation techniques have been applied at all Mach numbers from low subsonic to the hypersonic speed regime (from Mach 0.3 to Mach 8.0) and viscous effects have been added later through innovative simplified engineering formulations. In this case, starting from available mathematical formulations, new parametric equations have been developed to better capture the peculiarities of waverider configuration with integrated dorsal propulsive flow-path. The exploitation of simplified CFD simulations guarantees more reliable results without excessively compromising the available resources. Energies 2021, 14, x FOR PEER REVIEW 5 of 26

When dealing with conceptual design, due to the time and budget constraints, simplified approaches are preferred for the aerodynamic characterization, such as the Panel Methods. However, in this case, taking into account the complexity of the vehicle configuration, and remembering that one of the main goals of the H2020 STRATOFLY Project is to better investigate the behavior of the vehicle concept in subsonic and transonic speed regimes, simplified CFD simulation campaigns have been selected, as the most appropri- ate approach. Specifically, inviscid CFD simulation techniques have been applied at all Mach numbers from low subsonic to the hypersonic speed regime (from Mach 0.3 to Mach 8.0) and viscous effects have been added later through innovative simplified engineering formulations. In this case, starting from available mathematical formulations, new parametric equations have been developed to better capture the peculiarities of waverider configuration with integrated dorsal propulsive flow-path. The exploitation of simplified CFD simulations guarantees more reliable results without excessively compromising the available resources. Energies 2021, 14, 3580 5 of 28 3.2. Clean Configuration: Inviscid CFD and Innovative Viscous Corrections The first step of the build-up approach for the aerodynamic characterization of the 3.2.STARTOFLY Clean Configuration: MR3 vehicle Inviscid CFD consists and Innovative in the analysis Viscous Corrections of the clean configuration, i.e., the vehicle Theexternal first step layout of the including build-up approach empennages for the and aerodynamic undeflected characterization flight control of the surfaces. For the STARTOFLY MR3 vehicle consists in the analysis of the clean configuration, i.e., the vehicle externalclean configuration, layout including empennagesa Eulerian and unstructured undeflected flight grid control of about surfaces. one For million the clean of cells (half con- configuration,figuration) ahas Eulerian been unstructured generated gridby means of about of one ICEMCFD-TETRA million of cells (half configuration) grid generator (Figure 3). hasand been the generated commercial by means code of Fluent ICEMCFD-TETRA has been adopted grid generator for the (Figure numerical3). and thecalculations. Based commercialon past experiences code Fluent with has been very adopted similar for problems the numerical [7,8], calculations. the number Based of oncells past has been selected experiences with very similar problems [7,8], the number of cells has been selected to to guarantee a good compromise between calculation time and accuracy. Please note that guarantee a good compromise between calculation time and accuracy. Please note that aa grid grid convergence convergence analysis analysis has not has been not donebeen due done to thedue simplified to the simplified and preliminary and preliminary ap- approach.proach. However,However, a grid a grid error error less than less 10% than is expected 10% is [expected7]. However, [7]. grid However, convergence grid convergence analysisanalysis will will be carriedbe carried on as soonon as as soon high-fidelity as high-fidelity calculations calculations will be performed. will be performed.

FigureFigure 3. Inviscid3. Inviscid Grid. Grid. Half bodyHalf and body symmetry and symmetry plane. Cells plane. = 1 M. Cells = 1 M.

SomeSome results results are reportedare reported in the Figuresin the4 Figuresand5 where 4 and the results5 where of thethe inviscid results of the inviscid externalexternal CFD CFD simulations simulations are compared are compared with already with available already results available previously obtainedresults previously ob- by means of Supersonic/Hypersonic Panels Method (Surface Impact Method tool), based ontained classical by Modiﬁed-Newtonian, means of Supersonic Tangent-Wedge,/Hypersonic and Panels Shock-Expansion Method (Sur Theories.face Impact In the Method tool), supersonic-hypersonicbased on classical Modified-Newtonian, range down to Mach = 3, Tang the comparisonsent-Wedge, show and good Shock-Expansion results, at Theories. leastIn the for smallsupersonic-hypersonic angles of attack (i.e., the range case reported down into FiguresMach4 = and 3, 5the). The comparisons discrepancy show good re- betweensults, at the least two methodsfor small is expectedangles of to attack increase (i.e., for higher the case angles reported of attack. in However, Figures 4 and 5). The this is not the case for the STRATOFLY MR3 vehicle whose angle of attack throughout the mission is between −2◦ and +2◦.

EnergiesEnergies 2021 2021, 14, ,14 x ,FOR x FOR PEER PEER REVIEW REVIEW 6 of6 of26 26

discrepancydiscrepancy between between the the two two methods methods is isexpected expected to to increase increase for for higher higher angles angles of of attack. attack. Energies 2021, 14, 3580 However,However, this this is isnot not the the case case for for the the ST STRATOFLYRATOFLY MR3 MR3 vehicle vehicle whose whose angle angle of of attack attack6 of 28 throughoutthroughout the the mission mission is isbetween between −2° −2° and and +2°. +2°.

(a() a) (b()b )

FigureFigureFigure 4. 4. 4.LiftLift Lift (a ()(a aand)) andand Drag DragDrag (b (()bb coefficients)) coefﬁcientscoefficients versus versus versus Mach Mach Mach at at atαα =α = 0°.= 00°. ◦.

(a() a) (b()b )

FigureFigureFigure 5. 5. 5.PitchingPitching Pitching Moment MomentMoment (a ()(a aand)) andand Centre CentreCentre of of ofPressure Pressure Pressure (b ( b()b )versus) versus versus Mach Mach Mach at at atαα =α = 0°.= 00°. ◦.

AnAnAn updated updatedupdated mathematical mathematicalmathematical formulation formulationformulation for forfor viscous viscousviscous effect effecteffect corrective correctivecorrective factor factorfactor is isisdisclosed discloseddisclosed hereafter.hereafter.hereafter. The The The innovation innovation innovation lays lays lays in in the inthe fact the fact that fact that formulations, that formulations, formulations, already already already available available available in in the the liter- in liter- the ature,literature,ature, have have havebeen been modified been modified modified to to better better to bettercapture capture capture the the peculiarities thepeculiarities peculiarities of of highly highly of highly integrated integrated integrated wa- wa- veriderwaveriderverider configurations. configurations. configurations. The The viscous The viscous viscous effect effect effectis isadded added is added in in a seconda insecond a second step step by stepby means means by meansof of an an engi- ofengi- an neeringengineeringneering formula formula formula available available available in in the the literature in literature the literature ([10–12]) ([10–12]) ([10 which –which12]) can which can be be generalized can generalized be generalized as as in in Equa- Equa- as in tionEquationtion (4). (4). (4). ∆𝐶 𝛼∗ ∗ ∗, ∆𝐶 𝛼∗ 1..∗ ∗1 ∗ , Awet (4)(4) (∆C ) = α ∗ ∗ ∗ ∗ , (4) D viscext 2.58 2 γ [Log(Re)] (1 + β ∗ M ) Are f TheThe parametric parametric formulation formulation reported reported in in Equation Equation (4) (4) allows allows for for the the estimation estimation of of the the viscousviscousThe effect effect parametric by by correcting correcting formulation the the turbulent reportedturbulent flat inflat Equationplate plate theory theory (4) allows(represented (represented for the by estimation by the the term term of the viscous, see effect [10]) by with correcting (i) the thefactor turbulent flat which plate takes theory into (represented account the by compressi- the term . ., see [10]) with (i) the factor which takes into account the compressi- 1 ∗∗1 , see [10]) with (i) the factor γ which takes into account the compressibil- bility[bilityLog( effectRe effect)]2.58 [11], [11], (ii) (ii) the the wetted wetted and and the the reference(1 reference+β∗M2) areas areas ratio ratio and and (iii) (iii) the the parameter parameter 𝛼 𝛼will will beitybe customized customized effect [11], depending (ii) depending the wetted on on the and the vehicle thevehicle reference config configuration. areasuration. ratio In In the and the original (iii)original the formulation parameter formulationα whichwill which be wascustomizedwas used used to to support depending support the the Space on Space the Ship vehicle Ship 2 Aerodynamic2 configuration.Aerodynamic Characterization InCharacterization the original formulation [12], [12], the the values values which sug- wassug- gestedusedgested tofor for support these these parameters theparameters Space Shipare are as 2 as Aerodynamicfollows: follows: 𝛼 𝛼 Characterization 0.455, 0.455, 𝛽 = 𝛽 0.144, = 0.144, and [12 and], 𝛾0.65 the 𝛾0.65 values. . suggested forConsidering theseConsidering parameters the the substantial are substantial as follows: differences differencesα = 0.455, between betweenβ = 0.144, STRATOFLY STRATOFLY and γ = MR30.65. MR3 and and the the Space Space ShipShip 2 Consideringconfigurations,2 configurations, the substantiala newa new formulation formulation differences of of the between the parameters parameters STRATOFLY has has been been MR3 considered. considered. and the Space Firstly, Firstly, Ship the2the configurations,peculiar peculiar shape shape of a of newSTRATOFLY STRATOFLY formulation MR3 MR3 of prevents theprevents parameters use use of of Equation hasEquation been (4) considered.(4) for for the the entire entire Firstly, vehicle vehicle the peculiar shape of STRATOFLY MR3 prevents use of Equation (4) for the entire vehicle configuration, but it allows for applying it only at the external surface. Therefore, in this case the vehicle presented an integrated propulsive flow-path, the ratio Awet will be Are f evaluated by considering the external wetted area only, without taking into account the Energies 2021, 14, x FOR PEER REVIEW 7 of 26

Energies 2021, 14, 3580 7 of 28 configuration, but it allows for applying it only at the external surface. Therefore, in this case the vehicle presented an integrated propulsive flow-path, the ratio will be eval- integrated propulsiveuated flow-path,by considering which the characterizes external wetted STRATOFLY area only, without MR3 configuration. taking into account For the integrated propulsive flow-path, which characterizes STRATOFLY MR3 configuration. For STRATOFLY MR3, this leads to a value of about 2.31. Then, α, β, and γ coefficients have STRATOFLY MR3, this leads to a value of about 2.31. Then, 𝛼, 𝛽, and 𝛾 coefficients have been tuned to use a set of viscous CFD simulations carried out at angle of attack zero all been tuned to use a set of viscous CFD simulations carried out at angle of attack zero all over the range of Mach number. To achieve reliable results, the previous grid (Figure3) over the range of Mach number. To achieve reliable results, the previous grid (Figure 3) has been stretched close to the vehicle wall by adding a prism layer and thus reaching a has been stretched close to the vehicle wall by adding a prism layer and thus reaching a total number of cells of about 3.2 million. The k-ω-SST turbulence modeling, which can total number of cells of about 3.2 million. The k-ω-SST turbulence modeling, which can be be used for a wide range of fluid flows as in the present calculations (see [13]) has been used for a wide range of fluid flows as in the present calculations (see [13]) has been adopted. Pressure-far-fieldadopted. Pressure-far-field conditions have conditions been applied have b foreen the applied external for surfacesthe external of the surfaces of the domain (assigningdomain Mach (assigning number, Mach pressure, number, and pressure, temperature), and temperature), while the surfaces while the of thesurfaces of the vehicle are treatedvehicle as no-slip are treated adiabatic as no-slip walls. adiabatic The AUSM walls. scheme The AUSM (upwind) scheme for (upwind) numerical for numerical convective fluxconvective is used, coupled flux is used, with coupled a density-based with a density-based approach andapproach an implicit and an implicit time time dis- discretization thatcretization allows for that higher allows than for 1higher CFL number than 1 CFL (up tonumber 6). Considering (up to 6). Considering that viscous that viscous CFD runs requireCFD much runs more require CPU much time more than CPU the inviscidtime than Eulerian the inviscid ones, Eulerian the viscous ones, CFDthe viscous CFD runs have been performedruns have been only performed at angle of only attack at angle zero of for attack the tuning zero for of the previous tuningformula of previous formula (Equation (4)). Results(Equation of (4)). the Results viscous of external the viscous CFD external simulations CFD simulations carried out carried throughout out throughout the the reference trajectoryreference are trajectory reported are in reported blue in Figure in blue6 .in The Figure strange 6. The behavior strange ofbehavior the curve of the curve for for low Mach numberslow Mach is numbers mainly is due mainly to the due fact to the that fact for that each for Mach each Mach number, number, the CFD the CFD simula- simulation has beention has conducted been conducted keeping keeping the real the flight real flight altitude, altitude, resulting resulting therefore therefore in ain a different different ReynoldsReynolds number. number. In order In order to make to make the tuning the tuning easier, easier, the CFDthe CFD results results have have been been scaled to scaled to the samethe Reynolds same Reynolds number number (the value (the ofvalue Mach of Mach 0.3, which 0.3, which is 6.54 is× 6.5410 8×) 10 as8) reported as reported in green. in green. At theAt same the same time, time, the ( ∆theC )∆𝐶 predicted predicted using using the the original original formulation formulation has has been plot- D viscext been plotted (seeted the (see grey the line).grey line). Eventually, Eventually,α, β 𝛼,, and 𝛽, andγ coefficients 𝛾 coefficients have have been been tuned tuned to to better pre- better predict thedict trend the of trend the green of the line green through line through the analytical the analytical formulation, formulation, thus obtaining thus obtaining a a new new modified analyticalmodified formulation, analytical formulation, which is more which accurate is more for accurate wave-rider for configurations.wave-rider configurations. The curve obtainedThe atcurve the obtained end of the at tuningthe end process of the tuning is reported process in is red, reported and it in corresponds red, and it corresponds to Equation (4) withto Equationα = 0.43, (4) withβ = 𝛼0.31, 0.43, and γ 𝛽= 0.37.0.31, and 𝛾 0.37.

Figure 6. Tuning of engineeringFigure 6. Tuning formula of engineering for the (∆C formula) for. the ∆𝐶 . D viscext

This procedure cannotThis procedure be applied cannot to the be internalapplied to flow-path, the internal where flow-path, strong where section strong area section area variations causevariations significantly cause different significantly behavior different of the behavior air flow of with the air respect flow towith the respect simple to the simple flat plate. Therefore, for the internal part, the viscous internal CFD results are directly used, scaled only for the Reynolds effect, using Equation (5):

2.58 [Log(Re )] Awet C = nom ∗ Polynomial ∗ int D fint 2.58 CFD , (5) Are f [Log Re f light ] Energies 2021, 14, x FOR PEER REVIEW 8 of 26

flat plate. Therefore, for the internal part, the viscous internal CFD results are directly Energies 2021, 14, 3580 used, scaled only for the Reynolds effect, using Equation (5): 8 of 28 . 𝐶 . ∗ 𝑃𝑜𝑙𝑦𝑛𝑜𝑚𝑖𝑎𝑙 ∗ , (5)

where Renom is thewhere Reynolds 𝑅𝑒 number is the ofReynolds the reference number trajectory of the reference (used for trajectory CFD calculations), (used for CFD calcula- Re f light is the actualtions), trajectory 𝑅𝑒 Reynolds is the actual number, trajectory and ReynoldsPolynomial number,_CFD and is Polynomial_CFD the stepwise is the step- interpolation of CFDwise datainterpolation all along of the CFD Mach data number all along (Figure the Mach7). number (Figure 7).

Figure 7. Internal friction coefficient versus Mach. Figure 7. Internal friction coefficient versus Mach. The test matrix used to produce the results of the clean aero-database considers 16 Mach Numbers atThe 7 angles test matrix of attack used forto produce a total numberthe results of of 112 the runs. clean Theaero-database commer- considers 16 cial code Fluent hasMach been Numbers used runningat 7 angles on of CIRA attack Linux for a total Cluster number (“Turing” of 112 runs. 50 Teraflops, The commercial code 1440 computing cores)Fluent and has takingbeen used about running one day on forCIRA each Linu polarx Cluster with 16(“Turing” parallel 50 cores. Teraflops, 1440 computing cores) and taking about one day for each polar with 16 parallel cores. 3.3. Impact of Propulsive Flow Path 3.3. Impact of Propulsive Flow Path This section further exploits the CFD simulations already presented in the previous sections (that includesThis both section the externalfurther exploits and the the internal CFD simulations domain ofalready the vehicle) presented and in the previous provides suggestionssections on (that how includes to evaluate both the the contributionexternal and the of theinternal integrated domain propulsive of the vehicle) and pro- flow path which consistsvides suggestions of an intake, on how a combustor, to evaluate and the a nozzle,contribution all embedded of the integrated inside thepropulsive flow waverider vehiclepath layout. which As consists is reported of an in intake, Figure 8a, combusto the flow-pathr, and substantially a nozzle, all contributesembedded inside the waverider vehicle layout. As is reported in Figure 8, the flow-path substantially contributes Energies 2021, 14, x FOR PEER REVIEWto the overall aerodynamic forces, especially in subsonic, transonic, and low supersonic9 of 26 speed regimes. Theto the main overall effects aerodynamic are the additional forces, dragespecially and ain down-lift, subsonic, bothtransonic, mainly and due low supersonic speed regimes. The main effects are the additional drag and a down-lift, both mainly due to the intake. to the intake.

(a) (b)

FigureFigure 8. 8. DragDrag ( (aa)) and and Lift Lift ( (bb)) coefficients coefﬁcients versus versus Mach Mach at at αα == 0°. 0◦ .Comparison Comparison between between full full part part and and external external part. part.

TheThe sudden sudden reduction reduction of ofdrag drag at M at = M 4 =(Fig 4 (Figureure 8a) 8cana) canbe explained be explained because because the com- the bustorcombustor swallows swallows the shock the shockwave, wave,and in andaddition, in addition, the intake the down-lift intake down-lift disappears disappears (Figure 8b). The swallowing of the shock wave provides the aerodynamic characteristics with a hysteresis phenomenon, as can be seen in Figure 9. The investigated configuration shows that the shock wave is captured by the combustor between Mach 5 and Mach 6 during the ascent trajectory, while it is expelled between Mach 4 and Mach 3 during the descent trajectory. This different behavior of the air-intake can be noted in Figure 10 where we can see the Mach number contours at M = 4 and AoA = 0° far field conditions during ascent and descent phases. However, looking at the envisaged in-flight operations of the MR3 propulsion subsystem, only the descending branch of the hysteresis graph has been considered. Indeed, the ATR ducts are expected to be open, thus facilitating the entrance of the shock wave into the combustor between Mach 3 and Mach 4.

(a) (b) Figure 9. Drag coefficient (a) and Lift-to-Drag ratio (b) versus Mach at α = 0°. Comparison between full part and external part.

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(a) (b) Figure 8. Drag (a) and Lift (b) coefficients versus Mach at α = 0°. Comparison between full part and external part. Energies 2021, 14, 3580 9 of 28 The sudden reduction of drag at M = 4 (Figure 8a) can be explained because the combustor swallows the shock wave, and in addition, the intake down-lift disappears (Figure 8b). The swallowing of the shock wave provides the aerodynamic characteristics with a (Figure8b). The swallowing of the shock wave provides the aerodynamic characteristics hysteresis phenomenon, as can be seen in Figure 9. The investigated configuration shows with a hysteresis phenomenon, as can be seen in Figure9. The investigated configuration that the shock wave is captured by the combustor between Mach 5 and Mach 6 during the shows that the shock wave is captured by the combustor between Mach 5 and Mach ascent trajectory, while it is expelled between Mach 4 and Mach 3 during the descent tra- 6 during the ascent trajectory, while it is expelled between Mach 4 and Mach 3 during the jectory. This different behavior of the air-intake can be noted in Figure 10 where we can descent trajectory. This different behavior of the air-intake can be noted in Figure 10 where see the Mach number contours at M = 4 and AoA = 0° far field conditions during ascent we can see the Mach number contours at M = 4 and AoA = 0◦ far field conditions during andascent descent and descent phases. phases. However, However, looking looking at the atenvisaged the envisaged in-flight in-flight operations operations of the ofMR3 the propulsionMR3 propulsion subsystem, subsystem, only the only descending the descending branch branch of the of hysteresis the hysteresis graph graph has been has beencon- sidered.considered. Indeed, Indeed, the theATR ATR ducts ducts are are expected expected to tobe be open, open, thus thus facilitating facilitating the the entrance entrance of thethe shock shock wave wave into into the the combustor between Mach 3 and Mach 4.

(a) (b)

EnergiesFigure 2021, 14 9., x Drag FOR PEERcoefficient REVIEW (a) and Lift-to-Drag ratio (b) versus Mach at α = 0°. Comparison◦ between full part and external10 of 26 Figure 9. Drag coefﬁcient (a) and Lift-to-Drag ratio (b) versus Mach at α = 0 . Comparison between full part and part.external part.

(a) (b)

FigureFigure 10. 10. AscentAscent (a ()a and) and Descent Descent (b ()b Mach) Mach number number contour contour on on symmetry symmetry plane plane at at M M = =4 4and and α α= =0° 0 far◦ far field ﬁeld conditions. conditions.

3.4.3.4. Impact Impact of ofControl Control Surfaces Surfaces TheThe effect effect of of control control surfaces surfaces is istaken taken into into account account through through a asimplified simplified approach approach (inviscid(inviscid calculations) calculations) and and simplified simplified configuration configuration selecting onlyonly thethe partsparts ofof thethe vehicle vehicle of ofinterest. interest. For For example, example, for for the the effect effect of of flaps, flaps, a wing-flapa wing-flap configuration configuration is used is used (Figure (Figure 11a ), 11a),while while for for the the canard, canard, a stand-alonea stand-alone one. one. As As farfar asas the body-flap body-flap is is concerned, concerned, a amore more complexcomplex configuration configuration has has been been generated, generated, accounting forfor bothboth thethe rear rear part part of of the the fuselage fuse- lageand and the the vertical vertical tail tail (Figure (Figure 11b). 11b). Viscous Viscous corrections corrections are notare considered,not considered, since since the deltathe deltavalues values (with (with respect respect to the to cleanthe clean configuration) configuration) are used.are used. From Figures 12–14, the effect of control surfaces is reported. The contribution of the control surfaces is evaluated with respect to the clean configuration case (undeflected control surfaces); this effect is referred here as ΔCL and ΔCD. There is good agreement with the Surface Impact Method (SIM) except for with the body-flap configuration, which is due to the strong effect of fuselage and vertical tail not considered by SIM (Figure 14).

(a) (b) Figure 11. Simplified configuration of the Wing-Flap (a) and Body-Flap (b).

(a) (b)

Figure 12. ΔCL (a) and ΔCD (b) due to the flap effect at α = 0° and flap = −20°. Compared with SIM method in supersonic regime.

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(a) (b) Figure 10. Ascent (a) and Descent (b) Mach number contour on symmetry plane at M = 4 and α = 0° far field conditions.

3.4. Impact of Control Surfaces The effect of control surfaces is taken into account through a simplified approach (inviscid calculations) and simplified configuration selecting only the parts of the vehicle of interest. For example, for the effect of flaps, a wing-flap configuration is used (Figure 11a),(a) while for the canard, a stand-alone one. As far as the(b) body-flap is concerned, a more complex configuration has been generated, accounting for both the rear part of the fuse- Figure 10. Ascent (a) and Descent (b) Mach number contour on symmetry plane at M = 4 and α = 0° far field conditions. lage and the vertical tail (Figure 11b). Viscous corrections are not considered, since the delta3.4. Impact values of (withControl respect Surfaces to the clean configuration) are used. From Figures 12–14, the effect of control surfaces is reported. The contribution of the The effect of control surfaces is taken into account through a simplified approach control(inviscid surfaces calculations) is evaluated and simplified with respect configuration to the clean selecting configuration only the parts case of (undeflectedthe vehicle control surfaces); this effect is referred here as ΔCL and ΔCD. There is good agreement with Energies 2021, 14, 3580 of interest. For example, for the effect of flaps, a wing-flap configuration is used (Figure10 of 28 the11a), Surface while forImpact the canard, Method a stand-alone (SIM) except one. forAs farwith as thethe body-flap body-flap is concerned,configuration, a more which is duecomplex to the configuration strong effect has of beenfuselage generated, and vert accountingical tail notfor bothconsidered the rear by part SIM of the(Figure fuse- 14). lage and the vertical tail (Figure 11b). Viscous corrections are not considered, since the delta values (with respect to the clean configuration) are used. From Figures 12–14, the effect of control surfaces is reported. The contribution of the control surfaces is evaluated with respect to the clean configuration case (undeflected control surfaces); this effect is referred here as ΔCL and ΔCD. There is good agreement with the Surface Impact Method (SIM) except for with the body-flap configuration, which is due to the strong effect of fuselage and vertical tail not considered by SIM (Figure 14).

(a) (b)

FigureFigure 11. 11. SimplifiedSimpliﬁed conﬁgurationconfiguration of of the the Wing-Flap Wing-Flap (a) and (a) Body-Flapand Body-Flap (b). (b).

From Figures 12–14, the effect of control surfaces is reported. The contribution of the control surfaces is evaluated with respect to the clean conﬁguration case (undeﬂected

control surfaces); this effect is referred here as ∆CL and ∆CD. There is good agreement (witha) the Surface Impact Method (SIM) except for with the( body-ﬂapb) conﬁguration, which Figureis due11. Simplified to the strong configuration effect of fuselageof the Wing-Flap and vertical (a) and tail Body-Flap not considered (b). by SIM (Figure 14).

(a) (b)

Figure 12. ΔCL (a) and ΔCD (b) due to the flap effect at α = 0° and flap = −20°. Compared with SIM method in supersonic regime.

(a) (b)

EnergiesFigure 2021, 14 12., x ΔFORCL (PEERa) and REVIEW ΔCD (b ) due to the flap effect at α = 0° and ◦flap = −20°. Compared◦ with SIM method in supersonic11 of 26 Figure 12. ∆CL (a) and ∆CD (b) due to the ﬂap effect at α = 0 and ﬂap = −20 . Compared with SIM method in supersonicregime. regime.

(a) (b)

Figure 13. CL (a) and CD (b) due to the canard effect at several angle of attack. Figure 13. CL (a) and CD (b) due to the canard effect at several angle of attack.

(a) (b)

Figure 14. ΔCL (a) and ΔCD (b) due to the body-flap effect at α = 0° and several values of body-flap. Compared with SIM method in supersonic regime.

4. Mission Analysis The Aerodynamic analysis performed for the STRATOFLY MR3 vehicle is complemented by a parallel mission analysis which exploits the available aerodynamic database. As the complexity of the aerodynamic model increases and consequently, the aerodynamic database, the accuracy of the results of the mission simulations increases as well. In the following subsections, details on the mission simulation, performed with ASTOS 9.17, are provided.

4.1. Methodology Overview The mission analysis is carried out mirroring the steps of the build-up approach used for the aerodynamic database, and three main steps can be identified. First, a preliminary mission simulation is run considering only the aerodynamic data of the vehicle clean configuration, which does not take into account the deflection of the flight control surfaces or any aerodynamic contributions due to propulsive system components. A very first estimation of the vehicle performance along the trajectory can be evaluated in the preliminary phases of the Aerodynamic Analysis. Then, once the contribution of the flight control surfaces is added to the aerodynamic database, a more detailed mission simulation can be performed. However, one main lim- itation exists: ASTOS does not include the possibility to perform a static stability and trim analysis. For that reason, the trimmed conditions are separately evaluated through a Matlab script for each Mach number, and then used to create the trimmed aerodynamic database. Therefore, as final step, different mission simulations are carried out, considering the trimmed aerodynamic database and different possible routes. A detailed description of the vehicle model, including aerodynamics and propulsion characteristics, flight phases, and constraints are provided as inputs to the software for

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Energies 2021, 14, 3580 (a) (b) 11 of 28

Figure 13. CL (a) and CD (b) due to the canard effect at several angle of attack.

(a) (b)

◦ Figure 14. ∆ΔCL ((a)) and Δ∆CD ((bb)) due due to to the the body-flap body-ﬂap effect at α = 0° 0 andand several values of body-flap. body-ﬂap. Compared with SIM method in supersonic regime.

4. Mission Analysis The Aerodynamic analysis performed performed for for the the STRATOFLY STRATOFLY MR3 vehicle is complemented by a parallel mission analysis analysis which which ex exploitsploits the the available available aerodynamic aerodynamic database. database. As thethe complexitycomplexity of of the the aerodynamic aerodynamic model model increases increases and and consequently, consequently, the aerodynamic the aerody- namicdatabase, database, the accuracy the accuracy of the of results the results of the of mission the mission simulations simulations increases increases as well. as well. In the In thefollowing following subsections, subsections, details details on on the the mission mission simulation, simulation, performed performed withwith ASTOSASTOS 9.17, are provided.

4.1. Methodology Overview The mission analysis is carried out mirroring the steps of the build-up approach used for the aerodynamic database, and three main stepssteps cancan bebe identified.identified. First, a preliminary mission simulation is run considering only the aerodynamic data of the the vehicle vehicle clean clean configuration, configuration, which which does does not not take take into into account account the thedeflection deflection of the of flightthe flight control control surfaces surfaces or any or aerodynamic any aerodynamic contributions contributions due to due propulsive to propulsive system system components.components. A very A very first first estimation estimation of ofthe the vehi vehiclecle performance performance along along the the trajectory trajectory can can be evaluated in the preliminary phasesphases of the Aerodynamic Analysis. Then, once the contribution of the flight flight co controlntrol surfaces is added to the aerodynamic database, a a more more detailed detailed mission mission simulation simulation can can be beperformed. performed. However, However, one onemain main lim- itationlimitation exists: exists: ASTOS ASTOS does does not include not include the possib the possibilityility to perform to perform a static a static stability stability and trim and analysis.trim analysis. For that For thatreason, reason, the thetrimmed trimmed cond conditionsitions are are separately separately evaluated evaluated through through a Matlab script for each Mach number, and thenthen used to createcreate thethe trimmedtrimmed aerodynamicaerodynamic database. Therefore, asas finalfinal step,step, different different mission mission simulations simulations are are carried carried out, out, considering consider- ingthe trimmedthe trimmed aerodynamic aerodynamic database database and and different different possible possible routes. routes. A detailed description of the vehicle model model,, including aerodynamics and propulsion characteristics, flightflight phases,phases, and and constraints constraints are are provided provided as as inputs inputs to theto the software software for thefor mission simulation. For all the simulations, the standard atmosphere model contained in ASTOS has been used, and no cross winds have been considered. The vehicle structural mass is equal to 218.75 Mg, while the propellant mass is 181.25 Mg. The maximum take-off weight is then equal to 400 Mg [2]. The propulsive database contains the data of the ATR and DMR engines, and it is derived from LAPCAT MR2 project. Moreover, the angle of attack and the throttle are the two parameters which are used to control the vehicle throughout the simulation. The AoA is set to vary in the range −2◦/+2◦, while the throttle can vary between 0 (engine-off conditions) and 1 (full thrust). Based on the LAPCAT MR2.4 reference vehicle and mission [5], the STRATOFLY MR3 vehicle has been originally conceived to cover antipodal routes with a range up to 19,000 km, such as a Brussels to Sydney mission. However, as the aerodynamic database accuracy increases, the simulations show a detrimental effect for the vehicle aerodynamic performance due to the more accurate modelling of the propulsion flow-path. These effects Energies 2021, 14, 3580 12 of 28

practically prevent the MR3 vehicle from meeting the antipodal range. Therefore, a shorter mission connecting Brussels to Tokyo is also considered, with a range of approximately 12,000 km. The vehicle initial conditions are reported in Table2.

Table 2. Initial condition for mission simulation.

Initial Condition Value Latitude 50.9◦ Longitude 4.49◦ Altitude 0 m Velocity 128 m/s Heading −15◦

The simulation starts at the end of the take-off phase, as the runway acceleration at take-off cannot be properly simulated in ASTOS. An initial velocity of 128 m/s is set to ensure lift-off and to guarantee the stability of the trajectory simulation.

4.2. Mission Analysis with Clean Conﬁguration Energies 2021, 14, x FOR PEER REVIEW 13 of 26 The first set of mission simulations is run considering the initial version of the aerodynamic database, which is referred to the vehicle clean configuration only. A complete view of the mission trajectory is reported in Figure 15, where the line is colored by Mach numbers.

Figure 15. BRU-SYD mission trajectory. Figure 15. BRU-SYD mission trajectory. The Mach and altitude profiles are reported in Figures 16 and 17. The vehicle performs Thethe Mach hypersonic and altitude cruise profiles at M = are 8 and report an altitudeed in Figures that varies 16 and from 17. 31The to vehicle 36.8 km. per- The latter forms thealtitude hypersonic is higher cruise than at theM = 35 8 and km maximuman altitude altitude that varies of the from reference 31 to 36.8 mission km. The profile and latter altitudethis is is mainly higher due than to the the 35 higher km maxi liftmum coefficient altitude during of the the reference climb phase. mission The profile total mission and this timeis mainly is equal due to to 2 the h 52 higher m (10,300 lift co s).efficient during the climb phase. The total mission time is equal to 2 h 52 m (10,300 s). The Lift-to-Drag ratio profile is shown in Figure 18. The maximum L/D is equal to 9 and it is reached during the subsonic flight. However, the L/D drops to the minimum value of 4 during the supersonic climb between Mach 2 and 3, where the aerodynamic performances are very poor. Then, during the hypersonic cruise the L/D is increasing to 7.8. The final part of the mission involves an unpowered descent. The internal duct is empty, and the air flows through the internal duct, negatively affecting the overall aerodynamic characteristics of the vehicle. This results in a poor aerodynamic performance in engine-off conditions, where the L/D ranges between 3 and 5. The angle of attack used during the simulation is reported in Figure 19. During the climb phases, the AoA is set to negative values to limit the excess of lift which is produced due to the large vehicle surface. If the vehicle flew at higher angles of attack, it would quickly increase its altitude. Conversely, during the unpowered descent, the AoA is set to the maximum value of 2°. During this phase, since the Lift-to-Drag ratio is very low, it is necessary to increase the lift generated by the vehicle as much as possible, to avoid a steep descent. The value of the propellant mass contained on-board at each instant is reported in Figure 20. The highest fuel consumption rate is experienced during the supersonic and hypersonic climb, where the thrust is increased up to the maximum available thrust. Al- most all fuel is burnt during the mission and only 1 Mg is left at the end of the last propelled phase (Hypersonic cruise). These results seem to be not promising, considering that the clean configuration represent the best-case scenario for what concerns the aerodynamic performance. If the flight control surfaces contribution is added to the aerodynamic database, the aerodynamic performance degrades, and the fuel consumption increases.

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Figure 16. Mach number vs. mission time for clean configuration. Figure 16. Mach number vs. mission time for clean conﬁguration. Figure 16. Mach number vs. mission time for clean configuration.

Figure 17. Altitude vs. mission time for clean configuration. Figure 17. Altitude vs. mission time for clean configuration. FigureThe 17. Lift-to-Drag Altitude ratio vs. profile mission is shown time in Figurefor clean 18. The configuration. maximum L/D is equal to 9 and it is reached during the subsonic flight. However, the L/D drops to the minimum value of 4 during the supersonic climb between Mach 2 and 3, where the aerodynamic performances are very poor. Then, during the hypersonic cruise the L/D is increasing to 7.8. The final part of the mission involves an unpowered descent. The internal duct is empty, and the air flows through the internal duct, negatively affecting the overall aerodynamic characteristics of the vehicle. This results in a poor aerodynamic performance in engine-off conditions, where the L/D ranges between 3 and 5. The angle of attack used during the simulation is reported in Figure 19. During the climb phases, the AoA is set to negative values to limit the excess of lift which is produced due to the large vehicle surface. If the vehicle flew at higher angles of attack, it would quickly increase its altitude. Conversely, during the unpowered descent, the AoA is set to the maximum value of 2◦. During this phase, since the Lift-to-Drag ratio is very low, it is necessary to increase the lift generated by the vehicle as much as possible, to avoid a steep descent.

Figure 18. Lift-to-Drag ratio vs. mission time for clean configuration. Figure 18. Lift-to-Drag ratio vs. mission time for clean configuration.

Figure 19. Angle of attack vs. mission time for clean configuration. Figure 19. Angle of attack vs. mission time for clean configuration.

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Figure 16. Mach number vs. mission time for clean configuration. Figure 16. Mach number vs. mission time for clean configuration.

Figure 17. Altitude vs. mission time for clean configuration. Energies 2021, 14, 3580 14 of 28 Figure 17. Altitude vs. mission time for clean configuration.

FigureFigure 18. 18.Lift-to-Drag Lift-to-Drag ratio vs. missionratio timevs. formission clean conﬁguration. time for clean configuration. Figure 18. Lift-to-Drag ratio vs. mission time for clean configuration.

Figure 19. Angle of attack vs. mission time for clean configuration. FigureThe 19. value Angle of the of propellant attack massvs. mission contained on-boardtime for at clean each instant configuration. is reported in Figure 20 .19. The Angle highest fuelof attack consumption vs. mission rate is experienced time for during clean the configuration. supersonic and hypersonic climb, where the thrust is increased up to the maximum available thrust. Almost all fuel is burnt during the mission and only 1 Mg is left at the end of the last propelled phase (Hypersonic cruise). These results seem to be not promising, considering that the clean configuration represent the best-case scenario for what concerns the aerodynamic performance. If the flight control surfaces contribution is added to the aerodynamic database, the aerodynamic performance degrades, and the fuel consumption increases.

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FigureFigure 20. 20.Propellant Propellant mass vs. mass mission vs. time mission for clean configuration. time for clean configuration. 4.3. Trim Analysis Once the complete aerodynamic database has been delivered, the static longitudinal 4.3.stability Trim and Analysis trim analysis has been performed. This activity is crucial for the design of a civil passengerOnce the aircraft complete that is expected aerodynamic to fly stable through database the mission has phases. been However, delivered, the static longitudinal it has to be noticed that the need to fly through different speed regimes and the peculiarities stabilityof high-speed and vehicle trim configurations, analysis has and thereforebeen performed. the Center of Gravity This (CoG)activity shift is crucial for the design of a civilthroughout passenger the mission, aircraft may suggest that relaxing is expected the stability to requirements, fly stable taking through advantage the mission phases. However, from the modern guidance and navigation equipment. it hasThe to complete be noticed aerodynamic that database the need is composed to fly of through different contributions, different namely speed regimes and the peculiar- the clean configuration and the flight control surfaces (canards, flaps, and bodyflap). The itiesviscous of correctionhigh-speed is also addedvehicle for thecon dragfigurations, coefficient. An and additional therefore contribution the isCenter of Gravity (CoG) shift throughoutconsidered when the evaluating mission, the pitching may moment suggest coefficient relaxingCMy. Since the the thrust stability vector is requirements, taking ad- vantagenot aligned from with the the vehicle modernx-axis, the guidance thrust produces and a not navigation negligible pitching equipment. moment. The complete aerodynamicCM_T = −C databaseT·∆z/L is composed of different(6) contributions, namely

thewhere cleanCT is theconfiguration thrust force coefﬁcient, and ∆thez is theflightz distance control between surfaces the thrust vector(canards, and flaps, and bodyflap). The the vehicle x-axis, and L is the vehicle length. viscousThe propulsive correction database is alreadyalso added contains thefor net the thrust, drag which co isefficient. evaluated considering An additional contribution is con- sideredboth the gross when thrust evaluating and the contribution the of pitching the internal drag.moment Thus, the coefficient thrust contribution CMy. Since the thrust vector is notto the aligned total CD is with not considered the vehicle here. Moreover, x-axis, the the thrust thrust is supposed produces to be applied a alongnot negligible pitching moment. the x-axis, and it does not contribute to the total CL. The total value of the aerodynamic coefficients CL, CD, and CMy is evaluated as the sum𝐶𝑀_ of𝑇 the𝐶 different𝑇 ∙Δ𝑧 contributions:⁄𝐿 (6) CL = CL clean + CL f lap + CL canard + CL body f lap (7)

where CT isC Dthe= thrustCD clean + forceCD f lap +coefficient,CD canard + CD bodyΔz f lapis+ theCD viscous z distance (8)between the thrust vector and

the vehicleC Mx-axis,= CM cleanand+ CLM is f lap the+ C Mvehicle canard + C Mlength. body f lap + C M Thrust (9) TheThe different propulsive contributions database are also listed already in Table3 .contains the net thrust, which is evaluated considering both the gross thrust and the contribution of the internal drag. Thus, the thrust contribution to the total CD is not considered here. Moreover, the thrust is supposed to be applied along the x-axis, and it does not contribute to the total CL. The total value of the aerodynamic coefficients CL, CD, and CMy is evaluated as the sum of the different contributions:

𝐶 𝐶 𝐶 𝐶 𝐶 (7)

𝐶 𝐶 𝐶 𝐶 𝐶 𝐶 (8)

𝐶 𝐶 𝐶 𝐶 𝐶 𝐶 (9)

The different contributions are also listed in Table 3.

Table 3. Aerodynamic coefficients.

Clean Viscous Thrust Coefficient Canards Flaps Bodyflap Config Correction Correction CL x x x x CD x x x x x CMy x x x x x

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Table 3. Aerodynamic coefﬁcients.

Clean Viscous Thrust Coefficient Canards Flaps Bodyflap Config Correction Correction

CanardsCL andx flaps deflection x ranges x between x −20° and +20°, while the bodyflap de- CD x x x x x flectionCMy is in thex range −30°/0°. The x resulting x total x CMy is evaluated x for each possible combination of surfaces deflections and for the entire Mach range. The aim is to understand Canards and flaps deflection ranges between −20◦ and +20◦, while the bodyflap which conditions guarantee◦ ◦ longitudinal static stability, namely 𝛿𝐶⁄𝛿𝛼 0, at a given deflection is in the range −30 /0 . The resulting total CMy is evaluated for each possible Machcombination number of surfaces and deflections CoG andposition. for the entire The Mach latter range. Theis aimderived is to understand from the preliminary CoG shift which conditions guarantee longitudinal static stability, namely δCMy/δα < 0, at a given modelMach number which and has CoG position.been evaluated The latter is derived by fromPoliTO. the preliminary A specific CoG shift value model of the CoG position is con- sideredwhich has for been each evaluated Mach by PoliTO. number, A specific as value reported of the CoG in position Figure is considered 21. for each Mach number, as reported in Figure 21.

Figure 21. CoG position at different Mach numbers. Figure 21. CoG position at different Mach numbers. Then, the trim analysis can be performed. Among the full set of stable conditions evaluated during the previous step, it is possible to select the surfaces deflections and the correspondingThen, the angletrim of analysis attack αtrim canwhich be guarantee performed.CMy = 0. TheAmong first output the of full set of stable conditions this analysis is a set of trim maps, as the ones reported in Figures 22 and 23. The 3D evaluatedmap shows theduring resulting theαtrim previous, which corresponds step, toit theis possi trimmedble state, to as select a function the of surfaces deflections and the bodyflap and flap deflections, for Mach = 8 and CoG = 48 m. Each canard deflection δ corresponding angle of attack αtrim which guarantee CMy = canard0. The first output of this analy- is reported with a different color. Figure 23 also shows similar results. However, in this sisplot, is thea set bodyflap of trim deflection maps, is fixed as and the the ones angle ofreported attack αtrim variesin Figures only with 22 the and flap 23. The 3D map shows the deflection δ . resulting αflaptrim, which corresponds to the trimmed state, as a function of bodyflap and flap deflections, for Mach = 8 and CoG = 48 m. Each canard deflection δcanard is reported with a different color. Figure 23 also shows similar results. However, in this plot, the bodyflap deflection is fixed and the angle of attack αtrim varies only with the flap deflection δflap.

Figure 22. A 3D trim map example.

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Canards and flaps deflection ranges between −20° and +20°, while the bodyflap deflection is in the range −30°/0°. The resulting total CMy is evaluated for each possible combination of surfaces deflections and for the entire Mach range. The aim is to understand which conditions guarantee longitudinal static stability, namely 𝛿𝐶⁄𝛿𝛼 0, at a given Mach number and CoG position. The latter is derived from the preliminary CoG shift model which has been evaluated by PoliTO. A specific value of the CoG position is considered for each Mach number, as reported in Figure 21.

Figure 21. CoG position at different Mach numbers.

Then, the trim analysis can be performed. Among the full set of stable conditions evaluated during the previous step, it is possible to select the surfaces deflections and the corresponding angle of attack αtrim which guarantee CMy = 0. The first output of this analysis is a set of trim maps, as the ones reported in Figures 22 and 23. The 3D map shows the resulting αtrim, which corresponds to the trimmed state, as a function of bodyflap and flap deflections, for Mach = 8 and CoG = 48 m. Each canard deflection δcanard is reported with a different color. Figure 23 also shows similar results. However, in this plot, the bodyflap Energies 2021, 14, 3580 deflection is fixed and the angle of attack αtrim varies only17 ofwith 28 the flap deflection δflap.

Energies 2021, 14, x FOR PEER REVIEW 17 of 26

FigureFigure 22. 22.A 3D A trim 3D map trim example. map example.

FigureFigure 23.23.A A 2D 2D trim trim map example. map example. Since the STRATOFLY MR3 vehicle is supposed to fly at low angles of attack, only ◦ ◦ αtrimSincebetween the−2 STRATOFLYand 2 is considered MR3 for the analysis.vehicle For is each supposedαtrim the corresponding to fly at low angles of attack, only CL and CD can be also evaluated and, accordingly, the L/D. Moreover, for a given Mach αtrimnumber between and CoG − position,2° and the 2° same is consideredαtrim can be achieved for withthe differentanalysis. combinations For each of αtrim the corresponding CL Control Surfaces deflections. However, only one combination should be selected to be used andas anC inputD can for be the also mission evaluated simulation in ASTOS.and, accordingly, The combination that the corresponds L/D. Moreover, to the for a given Mach num- berhighest and L/D CoG is selected. position, the same αtrim can be achieved with different combinations of Con- Eventually, the complete trimmed aerodynamic database can be derived and used to trolperform Surfaces the mission deflections. simulation. The However, resulting CL,C onlyD and L/D,one atcombination different Mach numbers should be selected to be used as anand input for AoA for = 0 ◦the, are reportedmission in Figures simulation 24–26 for the in clean ASTOS. configuration The and combination the trimmed that corresponds to the case. The impact of the Control Surface deflections is clearly visible, especially for what highestconcerns L/D the increase is selected. in total drag and, consequently, the decrease in the aerodynamic Eventually, the complete trimmed aerodynamic database can be derived and used to perform the mission simulation. The resulting CL, CD and L/D, at different Mach numbers and for AoA = 0°, are reported in Figures 24–26. for the clean configuration and the trimmed case. The impact of the Control Surface deflections is clearly visible, especially for what concerns the increase in total drag and, consequently, the decrease in the aerodynamic efficiency along the entire Mach range. Eventually, an example of the database used in ASTOS is given in Table 4 where only some Mach numbers, representative of the different Mach regimes, are reported.

Figure 24. CL vs. Mach comparison between clean configuration and trimmed case.

Energies 2021, 14, x FOR PEER REVIEW 17 of 26

Figure 23. A 2D trim map example.

Since the STRATOFLY MR3 vehicle is supposed to fly at low angles of attack, only αtrim between −2° and 2° is considered for the analysis. For each αtrim the corresponding CL and CD can be also evaluated and, accordingly, the L/D. Moreover, for a given Mach number and CoG position, the same αtrim can be achieved with different combinations of Con- trol Surfaces deflections. However, only one combination should be selected to be used as an input for the mission simulation in ASTOS. The combination that corresponds to the highest L/D is selected. Eventually, the complete trimmed aerodynamic database can be derived and used to perform the mission simulation. The resulting CL, CD and L/D, at different Mach numbers and for AoA = 0°, are reported in Figures 24–26. for the clean configuration and the trimmed case. The impact of the Control Surface deflections is clearly visible, especially Energies 2021, 14, 3580 18 of 28 for what concerns the increase in total drag and, consequently, the decrease in the aerodynamic efficiency along the entire Mach range. Eventually, an example of the database usedefﬁciency in ASTOS along the is entire given Mach in range.Table Eventually,4 where only an example some of Mach the database numbers, used inrepresentative of the differentASTOS is givenMach in Tableregimes,4 where are only reported. some Mach numbers, representative of the different Mach regimes, are reported.

Energies 2021, 14, x FOR PEER REVIEW 18 of 26

Figure 24. CL vs. Mach comparison between clean conﬁguration and trimmed case. Figure 24. CL vs. Mach comparison between clean configuration and trimmed case.

Figure 25. CD vs. Mach comparison between clean configuration and trimmed case. Figure 25. CD vs. Mach comparison between clean conﬁguration and trimmed case. Figure 25. CD vs. Mach comparison between clean configuration and trimmed case.

Figure 26. L/D vs. Mach comparison between clean conﬁguration and trimmed case. Figure 26. L/D vs. Mach comparison between clean configuration and trimmed case. Figure 26. L/D vs. Mach comparison between clean configuration and trimmed case. Table 4. Excerpt of the trimmed aerodynamic database. Table 4. Excerpt of the trimmed aerodynamic database. δbodyflap Mach (-) Alpha (°) CL (-) CD (-) L/D (-) δflap (°) δcanard (°) CoG (m) δ(°)bodyflap Mach (-) Alpha (°) CL (-) CD (-) L/D (-) δflap (°) δcanard (°) CoG (m) 0.5 −2 0.118 0.021 5.49 4.15 11 −26(°) 53 0.50.5 0− 2 0.1600.118 0.0280.021 5.755.49 4.94.15 7 11 −29−26 5353 0.50.5 2 0 0.2200.160 0.0410.028 5.335.75 6.554.9 107 −30−29 5353 …0.5 … 2 …0.220 …0.041 …5.33 …6.55 …10 …−30 …53 0.95… −2… 0.121… 0.025… 4.83… −6.6… 16… −1… 51.5… 0.950.95 0− 2 0.1670.121 0.0310.025 5.434.83 −6.2−6.6 1316 −7− 1 51.551.5 0.950.95 2 0 0.2150.167 0.0410.031 5.295.43 −7.6−6.2 1213 −5− 7 51.551.5 …0.95 …2 …0.215 …0.041 …5.29 …−7.6 …12 …− 5 …51.5 3… −2… 0.036… 0.017… 2.14… 2.95… 20… −20… 50.5… 3 3 0− 2 0.0590.036 0.0160.017 3.772.14 −7.952.95 13 20 −23−20 50.550.5 3 3 2 0 0.1030.059 0.0230.016 4.583.77 −18.1−7.95 1613 −−423 50.550.5 …3 …2 …0.103 …0.023 …4.58 …−18.1 …16 …− 4 …50.5 8… −2… 0.020… 0.004… 5.37… −11.15… 12… −2… 48… 8 8 0− 2 0.0420.020 0.0060.004 7.055.37 −−7.5511.15 1312 −3− 2 4848 8 8 2 0 0.0640.042 0.0100.006 6.637.05 −10.4−7.55 1313 −5− 3 4848 8 2 0.064 0.010 6.63 −10.4 13 −5 48 4.4. Mission Analysis with Trimmed Configuration: BRU-SYD Mission Simulation 4.4.Once Mission the Analysis aerodynamic with Trimmed analysis Con is completefiguration:, further BRU-SYD mission Mission simulations Simulation can be performed,Once considering the aerodynamic the complete analysis trimmed is complete aerodynamic, further database.mission simulations The reference can trajec- be per- toryformed, is Brussels considering to Sydney the andcomplete the other trimmed input parametersaerodynamic are database. the same The used reference for the clean. trajec- Thetory new is Brussels simulation to Sydney shows andthat thethe otherfuel cons inpuumptiont parameters increases are the considerably same used forduring the clean. the The new simulation shows that the fuel consumption increases considerably during the

Energies 2021, 14, 3580 19 of 28

Table 4. Excerpt of the trimmed aerodynamic database.

Mach Alpha δ δ CoG C (-) C (-) L/D (-) δ (◦) canard bodyﬂap (-) (◦) L D ﬂap (◦) (◦) (m) 0.5 −2 0.118 0.021 5.49 4.15 11 −26 53 0.5 0 0.160 0.028 5.75 4.9 7 −29 53 0.5 2 0.220 0.041 5.33 6.55 10 −30 53 ...... 0.95 −2 0.121 0.025 4.83 −6.6 16 −1 51.5 0.95 0 0.167 0.031 5.43 −6.2 13 −7 51.5 0.95 2 0.215 0.041 5.29 −7.6 12 −5 51.5 ...... 3 −2 0.036 0.017 2.14 2.95 20 −20 50.5 3 0 0.059 0.016 3.77 −7.95 13 −23 50.5 Energies 2021, 14, x FOR PEER REVIEW 3 2 0.103 0.023 4.58 −18.1 16 −4 50.5 19 of 26 ...... 8 −2 0.020 0.004 5.37 −11.15 12 −2 48 8 0 0.042 0.006 7.05 −7.55 13 −3 48 8 2 0.064 0.010 6.63 −10.4 13 −5 48

entire4.4. mission, Mission Analysis as withreported Trimmed Configuration: in Figure BRU-SYD 27. As Mission a result, Simulation the vehicle runs out of fuel at approximately Once7700 the s aerodynamic (2 h 8 m), analysis while is complete, flying further the mission last simulations part of can the be per- hypersonic cruise. It is worth formed, considering the complete trimmed aerodynamic database. The reference trajectory notingis Brussels that tothe Sydney propulsive and the other input database parameters has are the remained same used for the unchanged clean. The in the simulations with new simulation shows that the fuel consumption increases considerably during the entire cleanmission, configuration as reported in Figureand 27 trimmed. As a result, theaerodynamic vehicle runs out of fueldatabase. at approximately Figure 28 shows the Mach number variation7700 s (2 h 8 m), with while range flying the (i.e., last part the of the distance hypersonic cruise.flown It is worthby the noting aircraft that during the mission), and the propulsive database has remained unchanged in the simulations with clean configu- the verticalration and dashed trimmed aerodynamic line represents database. Figure the 28 point shows the in Mach which number all variation the fuel is consumed. An estima- with range (i.e., the distance flown by the aircraft during the mission), and the vertical tion ofdashed the line maximum represents the point range in which achievable all the fuel is consumed.in these An conditions estimation of the can be obtained from these resultsmaximum which range is achievableequal to in theseapproximately conditions can be obtained 12,200 from km. these However, results which is it should also be highlighted equal to approximately 12,200 km. However, it should also be highlighted that the ASTOS that thesimulation ASTOS can be simulation continued even if can the fuel be mass continued becomes 0, so theeven results if fromthe that fuel point mass becomes 0, so the results fromon that are not point realistic. on are not realistic.

FigureFigure 27. 27. PropellantPropellant mass mass vs. Time vs. with Time Trimmed with aerodynamic Trimmed database. aerodynamic database.

Figure 28. Mach number vs. Range with Trimmed aerodynamic database.

The time needed to perform the climb phase is increasing considerably with respect to the previous simulation (Figure 29). This increment is due to the reduced aerodynamic performances, if compared to the clean configuration, as reported in Figure 30. The trimmed aerodynamic performances are poorer compared to those of the clean configuration: the L/D ratio ranges between 5 and 6 in the subsonic regime, while it drops below 3.5 during the supersonic climb. This highly affects the duration of the supersonic climb and limits the capability of the STRATOFLY MR3 vehicle to cover the antipodal route from Brussels to Sydney.

Figure 29. Mach number vs. mission time. Comparison between clean and trimmed configuration.

Energies 2021, 14, x FOR PEER REVIEW 19 of 26

entire mission, as reported in Figure 27. As a result, the vehicle runs out of fuel at approx- entireimately mission, 7700 sas (2 reported h 8 m), inwhile Figure flying 27. Asthe a lastresult, part the of vehicle the hypersonic runs out ofcruise. fuel atIt approx-is worth imatelynoting 7700that thes (2 propulsiveh 8 m), while database flying hasthe lastremained part of unchanged the hypersonic in the cruise. simulations It is worth with notingclean configurationthat the propulsive and trimmed database aerodynamic has remained database. unchanged Figure in28 theshows simulations the Mach withnum- cleanber variation configuration with andrange trimmed (i.e., the aerodynamic distance flo wndatabase. by the Figureaircraft 28 during shows the the mission), Mach num- and berthe variation vertical dashed with range line represents(i.e., the distance the point flo inwn which by the all aircraft the fuel during is consumed. the mission), An estima- and thetion vertical of the dashed maximum line representsrange achievable the point in inth whichese conditions all the fuel can is beconsumed. obtained An from estima- these tionresults of the which maximum is equal rangeto approximately achievable 12,200in these km. conditions However, can it should be obtained also be fromhighlighted these resultsthat the which ASTOS is equal simulation to approximately can be continued 12,200 even km. However,if the fuel massit should becomes also be 0, sohighlighted the results thatfrom the that ASTOS point simulation on are not can realistic. be continued even if the fuel mass becomes 0, so the results from that point on are not realistic.

Energies 2021, 14, 3580 20 of 28 Figure 27. Propellant mass vs. Time with Trimmed aerodynamic database. Figure 27. Propellant mass vs. Time with Trimmed aerodynamic database.

Figure 28. Mach number vs. Range with Trimmed aerodynamic database. Figure 28. Mach number vs. Range with Trimmed aerodynamic database. FigureThe 28. time Mach needed number to perform vs. the Range climb phase with is increasingTrimmed considerably aerodynamic with respect database. to the previous simulation (Figure 29). This increment is due to the reduced aerodynamic performances,The time if compared needed to the cleanto perform configuration, the as reportedclimb inphase Figure 30 is. The increasing trimmed considerably with respect toaerodynamic theThe previous time performances needed simulation are to poorer perform compared(Figure the to 29). thoseclimb This of the phase increment clean configuration: is increasing is due the to considerably the reduced withaerodynamic respect L/D ratio ranges between 5 and 6 in the subsonic regime, while it drops below 3.5 during toperformances,the the supersonic previous climb. simulationif compared (Figure to the 29). clean This confincrementiguration, is due as to reported the reduced in Figure aerodynamic 30. The performances,trimmedThis highly aerodynamic affects if thecompared duration performances of theto supersonicthe clean climbare confpoorer and limitsiguration, thecompared capability as of toreported those of in the Figure clean 30.configu- The the STRATOFLY MR3 vehicle to cover the antipodal route from Brussels to Sydney. trimmedration:However, the aerodynamic ifL/D the vehicle ratio performance ranges performances between is improved, are5 the and fuelpoorer 6 mass in consumption thecompared subsonic could to regime, those of while the clean it drops configu- below ration:3.5be reduced. during the AL/D the possible ratiosupersonic solution ranges could climb. between be to relax the5 and stability 6 in conditions the subsonic in the Mach regime, while it drops below range from 0.95 to 3, where the lift-to-drag ratio reaches the lowest value. Therefore, the 3.5constraint duringThis on longitudinalthehighly supersonic affects static stability the climb. isduration removed and of the the trim conditionssupersonic are evaluated climb and limits the capability of againThis in this highly range, considering affects the that δdurationCMy/δα > 0 .of The the resulting supersonic L/D is reported climb in and limits the capability of theFigure STRATOFLY 31, where the continuous MR3 line vehicle represents to the cover trim conditions the antipodal with static stability route and from Brussels to Sydney. thethe STRATOFLY dashed line refers to MR3 the unstable vehicle case. The to aerodynamic cover the efficiency antipodal is slightly route increasing from Brussels to Sydney. in this range, even if the increase is limited to values below 0.5.

Figure 29. Mach number vs. mission time. Comparison between clean and trimmed configuration. FigureFigure 29.29.Mach Mach number number vs. mission vs. time. mission Comparison time. between Comparison clean and trimmed between conﬁguration. clean and trimmed configuration.

Energies 2021, 14, x FOR PEER REVIEW 20 of 26

Energies 2021, 14, 3580 21 of 28

Figure 30. Lift-to-Drag ratio vs. Mach. Comparison between clean and trimmed configuration.

However, if the vehicle performance is improved, the fuel mass consumption could be reduced. A possible solution could be to relax the stability conditions in the Mach range from 0.95 to 3, where the lift-to-drag ratio reaches the lowest value. Therefore, the constraint on longitudinal static stability is removed and the trim conditions are evaluated again in this range, considering that 𝛿𝐶⁄𝛿𝛼 0. The resulting L/D is reported in Figure 31, where the continuous line represents the trim conditions with static stability and the dashed line refers to the unstable case. The aerodynamic efficiency is slightly increasing Figure 30. Lift-to-Drag ratio vs. Mach. Comparison between clean and trimmed conﬁguration. Figurein this range, 30. Lift-to-Drageven if the increase ratio is limited vs. Mach. to values Comparison below 0.5. between clean and trimmed configuration.

However, if the vehicle performance is improved, the fuel mass consumption could be reduced. A possible solution could be to relax the stability conditions in the Mach range from 0.95 to 3, where the lift-to-drag ratio reaches the lowest value. Therefore, the constraint on longitudinal static stability is removed and the trim conditions are evaluated again in this range, considering that 𝛿𝐶⁄𝛿𝛼 0. The resulting L/D is reported in Figure 31, where the continuous line represents the trim conditions with static stability and the dashed line refers to the unstable case. The aerodynamic efficiency is slightly increasing in this range, even if the increase is limited to values below 0.5.

Figure 31. Comparison of the Lift-to-Drag ratio between stable and unstable conditions in the Figure 31. Comparison of the Lift-to-Drag ratio between stable and unstable conditions in the su- supersonic Mach regime. personic Mach regime. A further simulation is then run considering the unstable trim conditions from M = 0.95 to MA =further 3, while simulation the same is set then of trim run dataconsidering is used forthe theunstable other Machtrim conditions numbers. Thefrom results M = 0.95are to reported M = 3, while in Figures the same 32 and set 33 of withtrim thedata dash-dot is used for line, the where other the Mach altitude numbers. and MachThe resultsprofiles are are reported compared in Figures to the 32 other and cases. 33 with The the time dash-dot needed line, to where perform the the altitude supersonic and Machclimb profiles decreases are tocompared 1040 s, a to mid-value the other withcases. respect The time to theneeded two previousto perform cases. the supersonic However, a climbsignificant decreases difference to 1040 still s, a existsmid-value if compared with respect to the to clean the two configuration previous cases. mission However, profile. a significantThe resultingdifference aerodynamic still exists if efficiencycompared is to reported the clean in configuration Figure 34. The mission L/D is profile. still low at supersonic speeds, but the vehicle is now able to accelerate in a shorter time. However, the overall fuel consumption is still too high. The vehicle runs out of fuel during the hypersonic cruise after 2 h 5 m (7500 s), while flying the last part of the hypersonic cruise (Figure 35). The altitude and Mach profile vs. range are reported in Figures 36 and 37, where the vertical dashed line shows the point where the fuel ends. The maximum range is equal to approximately 12,600 km.

Figure 31. Comparison of the Lift-to-Drag ratio between stable and unstable conditions in the supersonic Mach regime.

A further simulation is then run considering the unstable trim conditions from M = 0.95 to M = 3, while the same set of trim data is used for the other Mach numbers. The results are reported in Figures 32 and 33 with the dash-dot line, where the altitude and Mach profiles are compared to the other cases. The time needed to perform the supersonic climb decreases to 1040 s, a mid-value with respect to the two previous cases. However, a significant difference still exists if compared to the clean configuration mission profile.

Energies 2021, 14, x FOR PEER REVIEW 21 of 26

Energies 2021, 14, 3580 22 of 28

Figure 32. Altitude vs. mission time comparison for the three cases analyzed.

Figure 32. Altitude vs. mission time comparison for the three cases analyzed. Figure 32. Altitude vs. mission time comparison for the three cases analyzed.

Figure 33. Mach number vs. mission time comparison for the three cases analyzed. Figure 33. Mach number vs. mission time comparison for the three cases analyzed.

FigureThe 33. resulting Mach number aerodynamic vs. mission efficiency time compar is reportedison for the in three Figure cases 34. analyzed. The L/D is still low at supersonic speeds, but the vehicle is now able to accelerate in a shorter time. However, The resulting aerodynamic efficiency is reported in Figure 34. The L/D is still low at the overall fuel consumption is still too high. The vehicle runs out of fuel during the hy- supersonic speeds, but the vehicle is now able to accelerate in a shorter time. However, personic cruise after 2 h 5 m (7500 s), while flying the last part of the hypersonic cruise the overall fuel consumption is still too high. The vehicle runs out of fuel during the hy- (Figure 35). The altitude and Mach profile vs. range are reported in Figures 36 and 37, personic cruise after 2 h 5 m (7500 s), while flying the last part of the hypersonic cruise where the vertical dashed line shows the point where the fuel ends. The maximum range (Figure 35). The altitude and Mach profile vs. range are reported in Figures 36 and 37, is equal to approximately 12,600 km. where the vertical dashed line shows the point where the fuel ends. The maximum range is equal to approximately 12,600 km.

Energies 2021, 14, x FOR PEER REVIEW 21 of 26

Figure 32. Altitude vs. mission time comparison for the three cases analyzed.

Figure 33. Mach number vs. mission time comparison for the three cases analyzed.

The resulting aerodynamic efficiency is reported in Figure 34. The L/D is still low at supersonic speeds, but the vehicle is now able to accelerate in a shorter time. However, the overall fuel consumption is still too high. The vehicle runs out of fuel during the hypersonic cruise after 2 h 5 m (7500 s), while flying the last part of the hypersonic cruise (Figure 35). The altitude and Mach profile vs. range are reported in Figures 36 and 37, where the vertical dashed line shows the point where the fuel ends. The maximum range Energies 2021, 14, 3580 is equal to approximately 12,600 km. 23 of 28

Energies 2021, 14, x FOR PEER REVIEW 22 of 26

Figure 34. Lift-to-Drag ratio vs. mission time for trimmed AEDB with unstable conditions at supersonic Mach numbers. Figure 34. Lift-to-Drag ratio vs. mission time for trimmed AEDB with unstable conditions at super- sonicFigure Mach 34. Lift-to-Drag numbers. ratio vs. mission time for trimmed AEDB with unstable conditions at supersonic Mach numbers.

Figure 35. Propellant mass vs. mission time for trimmed AEDB with unstable conditions at super- sonicFigure Mach 35. Propellant numbers. mass vs. mission time for trimmed AEDB with unstable conditions at super- Figuresonic Mach 35. numbers. Propellant mass vs. mission time for trimmed AEDB with unstable conditions at supersonic Mach numbers.

FigureFigure 36. 36.Altitude Altitude vs. Range vs. for trimmedRange AEDB for withtrimmed unstable conditionsAEDB atwith supersonic unstable Mach numbers. conditions at supersonic Mach numbers. Figure 36. Altitude vs. Range for trimmed AEDB with unstable conditions at supersonic Mach numbers.

Figure 37. Mach number vs. Range for trimmed AEDB with unstable conditions at supersonic Mach numbers. Figure 37. Mach number vs. Range for trimmed AEDB with unstable conditions at supersonic Mach numbers.4.5. Mission Analysis with Trimmed Configuration: BRU-NRT Mission Simulation The results of the previous mission simulation suggest that the STRATOFLY MR3 4.5.vehicle Mission could Analysis not be with able Trimmed to complete Configuration: the 19,000 BRU-NRT km range Mission mission. Simulation For that reason, a shorterThe missionresults ofshould the previous also be considered. mission simu Thelation range suggest is decreased that the to about STRATOFLY 12,000 km MR3 and vehiclethe selected could routenot be is ableBrussels to complete to Tokyo the Narita 19,000 (BRU-NRT). km range Thismission. route For is thatchosen reason, since ait shorterallows missionthe vehicle should to fly also entirely be considered. over the sea The at range Mach is greater decreased than to 1, about as it also 12,000 happens km and for thethe selected BRU-SYD route mission. is Brussels An overview to Tokyo of Narita this tr ajectory(BRU-NRT). is reported This route in Figure is chosen 38. Thesince first it allowspart of the the vehicle mission to flyup entirelyto the Bering over the strait sea isat equivalentMach greater to thanthe previous 1, as it also case. happens From forthis thepoint BRU-SYD on, the vehiclemission. performs An overview a right of turn this heading trajectory towards is reported Tokyo. in Figure 38. The first part of the mission up to the Bering strait is equivalent to the previous case. From this point on, the vehicle performs a right turn heading towards Tokyo.

Energies 2021, 14, x FOR PEER REVIEW 22 of 26

Figure 34. Lift-to-Drag ratio vs. mission time for trimmed AEDB with unstable conditions at supersonic Mach numbers.

Figure 35. Propellant mass vs. mission time for trimmed AEDB with unstable conditions at supersonic Mach numbers.

Figure 36. Altitude vs. Range for trimmed AEDB with unstable conditions at supersonic Mach num- Energies 2021, 14, 3580 24 of 28 bers.

Figure 37. Mach number vs. Range for trimmed AEDB with unstable conditions at supersonic FigureMach numbers. 37. Mach number vs. Range for trimmed AEDB with unstable conditions at supersonic Mach numbers.4.5. Mission Analysis with Trimmed Configuration: BRU-NRT Mission Simulation The results of the previous mission simulation suggest that the STRATOFLY MR3 4.5.vehicle Mission could not Analysis be able to completewith Trimmed the 19,000 Con km rangefiguration: mission. ForBRU-NRT that reason, Mission a Simulation shorter mission should also be considered. The range is decreased to about 12,000 km and the selectedThe routeresults is Brussels of the to Tokyoprevious Narita (BRU-NRT).mission Thissimu routelation is chosen suggest since it that the STRATOFLY MR3 Energies 2021, 14, x FOR PEER REVIEWallows the vehicle to fly entirely over the sea at Mach greater than 1, as it also happens for 23 of 26 vehiclethe BRU-SYD could mission. not An overviewbe able of thisto trajectorycomplete is reported the in19 Figure,000 38 .km The firstrange part mission. For that reason, a shorterof the mission mission up to the should Bering strait also is equivalent be considered. to the previous The case. range From this is point decreased on, to about 12,000 km and the vehicle performs a right turn heading towards Tokyo. the selected route is Brussels to Tokyo Narita (BRU-NRT). This route is chosen since it allows the vehicle to fly entirely over the sea at Mach greater than 1, as it also happens for the BRU-SYD mission. An overview of this trajectory is reported in Figure 38. The first part of the mission up to the Bering strait is equivalent to the previous case. From this point on, the vehicle performs a right turn heading towards Tokyo.

Figure 38. BRU-NRT mission trajectory. Figure 38. BRU-NRT mission trajectory. The resulting altitude and Mach profiles are reported in Figures 39 and 40. The hypersonic cruise duration is 3100 s (52 min), a value that is shorter than the BRU-SYD The resulting altitude and Mach profiles are reported in Figures 39 and 40. The hy- case, due to the reduced range. Therefore, the altitude at the end of the cruise is limited personicto 35.5 km. cruise The totalduration mission is 3100 duration s (52 is min), equal a to value 2 h 17 that m (8200 is shorter s). The than propellant the BRU-SYD mass case, dueof 181.25 to the Mg reduced is sufficient range. to Therefore, cover the BRU-NRT the altitu mission,de at the and end the of residual the cruise propellant is limited at to 35.5 km.the endThe of total the mission is duration equal to 10.45is equal Mg, to as 2 can h 17 be m seen (8200 in Figure s). The 41 .propellant The L/D and mass AoA of 181.25 Mgprofiles is sufficient are reported to cover in Figures the BRU-NRT 42 and 43, respectively.mission, and the residual propellant at the end of the mission is equal to 10.45 Mg, as can be seen in Figure 41. The L/D and AoA profiles are reported in Figures 42 and 43, respectively.

Figure 39. Altitude vs. mission time for trimmed AEDB with unstable conditions at supersonic Mach numbers. BRU-NRT mission.

Figure 40. Mach number vs. mission time for trimmed AEDB with unstable conditions at supersonic Mach numbers.BRU-NRT mission.

Energies 2021, 14, x FOR PEER REVIEW 23 of 26

Figure 38. BRU-NRT mission trajectory.

FigureThe 38. resultingBRU-NRT altitudemission trajectory. and Mach profiles are reported in Figures 39 and 40. The hypersonic cruise duration is 3100 s (52 min), a value that is shorter than the BRU-SYD case, due toThe the resulting reduced altitude range. Therefore, and Mach theprofiles altitu ardee atreported the end inof Figuresthe cruise 39 isand limited 40. The to 35.5hy- personickm. The totalcruise mission duration duration is 3100 iss (52equal min), to 2 a h value 17 m that(8200 is s).shorter The propellant than the BRU-SYD mass of 181.25 case, dueMg isto sufficientthe reduced to coverrange. the Therefore, BRU-NRT the mission, altitude andat the the end residual of the propellantcruise is limited at the toend 35.5 of km.the missionThe total is mission equal to duration 10.45 Mg, is equal as can to be 2 hseen 17 m in (8200 Figure s). 41.The The propellant L/D and mass AoA of profiles 181.25 Mgare reportedis sufficient in Figuresto cover 42 the and BRU-NRT 43, respectively. mission, and the residual propellant at the end of the mission is equal to 10.45 Mg, as can be seen in Figure 41. The L/D and AoA profiles Energies 2021, 14, 3580 are reported in Figures 42 and 43, respectively. 25 of 28

Figure 39. Altitude vs. mission time for trimmed AEDB with unstable conditions at supersonic Mach numbers.Figure 39. BRU-NRTAltitude vs. mission mission. time for trimmed AEDB with unstable conditions at supersonic Mach numbers. BRU-NRT mission. Figure 39. Altitude vs. mission time for trimmed AEDB with unstable conditions at supersonic Mach numbers. BRU-NRT mission.

Energies 2021, 14, x FOR PEER REVIEW 24 of 26

Figure 40. Mach number vs. mission time for trimmed AEDB with unstable conditions at supersonic Mach numbers.BRU-NRT mission. Figure 40. Mach number vs. mission time for trimmed AEDB with unstable conditions at supersonic Mach numbers.BRU-NRT mission. Figure 40. Mach number vs. mission time for trimmed AEDB with unstable conditions at supersonic Mach numbers.BRU-NRT mission.

Figure 41. Propellant mass vs. mission time for trimmed AEDB with unstable conditions at super- Figuresonic 41. Mach Propellant numbers. BRU-NRT mass mission. vs. mission time for trimmed AEDB with unstable conditions at supersonic Mach numbers. BRU-NRT mission.

Figure 42. Lift-to-Drag ratio vs. mission time for trimmed AEDB with unstable conditions at supersonic Mach numbers. BRU-NRT mission.

Figure 43. Angle of attack vs. mission time for trimmed AEDB with unstable conditions at supersonic Mach numbers. BRU-NRT mission.

The following table (Table 5) summarizes the major results of the mission simulations performed in this study. The 3rd column has been added to highlight if the mission can be properly achieved with the available fuel on board. If this is possible, the distance flown, the residual fuel and the time needed to perform the mission are reported. Con- versely, the distance flown and time reported refer to the condition in which all the fuel is used.

Table 5. Overview of trajectory simulations results.

Aerodynamic Mission Distance Residual fuel Time Route Configuration Completed? flown (km) (Mg) (hr:min) Brussels to Clean Yes 18,200 1.00 2 h 52 m Sydney Trimmed and No 12,200 0.00 2 h 8 m

Energies 2021, 14, x FOR PEER REVIEW 24 of 26

Figure 41. Propellant mass vs. mission time for trimmed AEDB with unstable conditions at supersonic Mach numbers. BRU-NRT mission. Figure 41. Propellant mass vs. mission time for trimmed AEDB with unstable conditions at super- Energies 2021, 14, 3580 sonic Mach numbers. BRU-NRT mission. 26 of 28

Figure 42. Lift-to-Drag ratio vs. mission time for trimmed AEDB with unstable conditions at super- sonicFigure Mach 42. Lift-to-Drag numbers. ratio BRU-NRT vs. mission timemission. for trimmed AEDB with unstable conditions at Figuresupersonic 42. Lift-to-Drag Mach numbers. BRU-NRT ratio vs. mission. mission time for trimmed AEDB with unstable conditions at supersonic Mach numbers. BRU-NRT mission.

Figure 43. Angle of attack vs. mission time for trimmed AEDB with unstable conditions at supersonic Mach numbers. BRU-NRT mission. Figure 43. Angle of attack vs. mission time for trimmed AEDB with unstable conditions at super- The following table (Table5) summarizes the major results of the mission simulations sonicperformed Mach in numbers. this study. The BRU-NRT 3rd column mission. has been added to highlight if the mission can be Figureproperly 43. achieved Angle withof attack the available vs. mission fuel on board. time If this for is trimmed possible, the AEDB distance with flown, unstable conditions at super- theThe residual following fuel and the timetable needed (Table to perform 5) summarizes the mission are reported. the major Conversely, results the of the mission simulations sonicdistance Mach flown numbers. and time reportedBRU-NRT refer to mission. the condition in which all the fuel is used. performed in this study. The 3rd column has been added to highlight if the mission can Table 5. Overview of trajectory simulations results. be properlyThe following achieved table with (Table the 5) available summarizes fuel theon majorboard. results If this of is the possible, mission the simulations distance Aerodynamic Mission Distance Residual Time Route performedflown, the residualin Configurationthis study. fuelCompleted? and The the3rd time flowncolumn (km)needed hasfuel beento (Mg) perform added(hr:min) the to highlightmission are if the reported. mission Con- can Clean Yes 18,200 1.00 2 h 52 m beversely, properlyBrussels the to distanceachieved flown with andthe availabletime reported fuel referon board. to the If condition this is possible, in which the all distance the fuel Trimmed and Sydney No 12,200 0.00 2 h 8 m flown,is used. the residualstable fuel and the time needed to perform the mission are reported. Con- Trimmed and No 12,600 0.00 2 h 5 m versely, the distanceunstable flown and time reported refer to the condition in which all the fuel isTable used.Brussels 5. Overview to Trimmed of andtrajectory simulations results. Yes 12,245 10.45 2 h 17 m Tokyo unstable Aerodynamic Mission Distance Residual fuel Time TableRoute 5. Overview of trajectory simulations results. 5. Conclusions Configuration Completed? flown (km) (Mg) (hr:min) This paper provides technical insights on the aerodynamic characterization activities Brusselscoupled with to detailed Aerodynamic missionClean analysis simulations, Mission Yes performed in theDistance 18,200 field of the H2020Residual 1.00 fuel 2 Timeh 52 m Route Sydney ConfigurationTrimmed and Completed? No flown 12,200 (km) (Mg) 0.00 (hr:min) 2 h 8 m Brussels to Clean Yes 18,200 1.00 2 h 52 m Sydney Trimmed and No 12,200 0.00 2 h 8 m

Energies 2021, 14, 3580 27 of 28

STRATOFLY project, for the Mach 8 waverider reference configuration. Considering the complexity of the configuration to be analyzed at conceptual/preliminary design stage, a build-up approach has been adopted, incrementally increasing the complexity of the aerodynamic model, from the clean external configuration up to the complete configuration, including propulsion system elements and flight control surfaces. The comparison of the results obtained through the different mission analysis campaigns clearly shows that the accuracy of aerodynamic characterization may determine the feasibility or unfeasibility of the mission concept. It is worth noting that in all the simulations presented in the previous section, the descent was performed in engine-off conditions. However, due to the poor aerodynamic performance during this phase, the rate of descent could become too high. During the final part of the mission, the aerodynamic efficiency drops to values ranging between 2.5 and 5, causing the vehicle to quickly loose altitude. Therefore, the authors are currently working to remove the constraints on the unpowered descent, understanding the benefits of a sustained descent phase.

Author Contributions: Conceptualization, N.V. and R.F.; methodology, N.V., R.F., P.R. and O.G.; software, P.R. and O.G.; validation, R.F. and N.V.; formal analysis, P.R. and O.G.; writing—original draft preparation, O.G. and P.R.; writing—review and editing, R.F. and N.V.; visualization, R.F.; supervision, N.V.; project administration, N.V. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by European Union’s Horizon 2020 research and innovation programme under grant agreement No 769246—Stratospheric Flying Opportunities for High-Speed Propulsion Concepts (STRATOFLY) Project. Institutional Review Board Statement: Not Applicable. Informed Consent Statement: Not Applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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